Suppose that (X1, X2) are bivariate normal variables with zero mean, unit variance and unknown correlation . Show that A1 = X1 and A2 =

Suppose that (X1, X2) are bivariate normal variables with zero mean, unit variance and unknown correlation ρ. Show that A1 = X1 and A2 = X2 are each ancillary, though not jointly ancillary, and that neither is a component of the sufficient statistic. Let T =

X1 X2

. Show that